Method and apparatus for circuit pattern inspection

ABSTRACT

A system for measuring a pattern on a sample, including: a data processing system that processes a set of two-dimensional distribution data of intensities from the sample, to calculate: a set of edge points indicative of position of edges of the pattern in a two-dimensional plane from the two-dimensional distribution data; an approximation edge indicative of the edge of the pattern; an edge fluctuation data by calculating a difference between the set of edge points and the approximation edge; and a correlation between a first portion of the edge fluctuation data and a second portion of the edge fluctuation data.

CROSS REFERENCE TO RELATED APPLICATION

This is a continuation of U.S. application Ser. No. 10/071,097, filedFeb. 11, 2002 (now U.S. Pat. No. 7,095,884). This application relates toand claims priority from Japanese Patent Application No. 2001-224017,filed on Jul. 25, 2001. The entirety of the contents and subject matterof all of the above is incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates to a circuit pattern inspection techniqueand, more particularly, to a method and apparatus for observing a finepattern by using a scanning microscope and inspecting an edge shape ofthe fine pattern.

In an LSI process, particularly, a microfabrication process performedafter ArF lithography in recent years, as a pattern is becoming finer,the problem of roughness at the edge of a pattern is becoming bigger.

The occurrence of roughness is caused by the property of the materialitself, exposure equipment, a substrate, or an observing apparatusitself. In a mass production process, the degree of roughness exerts alarge influence on the performance of a product. Even when roughness isnot abnormally large, appearance of characteristic roughness is often areflection of deterioration in performance of a manufacturing apparatus,so that a failure may occur in a product in future. Consequently,development of a system for observing the shape of roughness at edges ofa pattern and specifying the cause from the characteristic of theroughness is urgently necessary. Considering that the system is used ina mass production process, the inspection method has to be anon-destructive one.

Conventionally, information is empirically obtained mainly by viewobservation of an observed image by a scanning electron microscope. Forexample, there is a case that a state where right and left edgesfluctuate synchronously can be seen at the time of observing a linepattern of a resist. In this case, the causes can be considered asfollows for example: due to a narrow line, the top of a patternfluctuates at the time of development, a light intensity distribution atthe time of exposure fluctuates, and the observed image itself isdistorted. There is also a case that roughness is seen relatively smallaround the surface but is seen large on the bottom portion of a pattern.From such a phenomenon, the possibility that the chemical property ofthe resist material does not match that of the substrate well and aresidual is caused is considered.

However, such criteria of determination are not quantitative, theconclusion varies depending on observers. In order to systematicallyanalyze the cause of occurrence of roughness without depending on theobserver, the shape of roughness has to be quantitatively determined.

An example of the conventional attempt to quantitatively express thecharacteristic of the shape of the pattern edge is disclosed in thedocument, “B. Su, T. Pan, P. Li, J. Chinn, X. Shi, and M. Dusa, Proc.1998 IEEE/SEMI Advanced Semiconductor Manufacturing Conference, p 259(1998)”. According to the method, the taper shape of a line pattern edgeis expressed by numbers from an SEM image. Although information of theedge portion in a cross sectional shape can be obtained to a certaindegree, the characteristic of an edge in the direction along a line edgecannot obtained. A value obtained is an index of inclination of a sideface of an edge, so that roughness cannot be evaluated.

A general method of detecting roughness of a pattern edge is a method ofobtaining some deviations of edge positions from a straight line andcalculating a standard deviation σ in a distribution of the deviationsor a value which is three times as large as σ. However, the roughnessherein denotes accurately a dimensional error as used in the documents,“S. Mori, T. Morisawa, N. Matsuzawa, Y. Kamimoto, M. Endo, T. Matsuo, K.Kuhara, and M. Sasago, J. Vac. Sci. Technol. B16, p 739 (1998)” and “C.H. Diaz, H. Tao, Y. Ku, A. Yen, and K. Young, IEEE Electron DeviceLetters 22, p 287 (2001)” and is not an index used to evaluate the shapeof an edge.

As described above, conventionally, there is no method of quantitativelyevaluating the shape of an edge. Although the stereoscopic shape of anedge can be determined by view observation, it depends on the observer.

SUMMARY OF THE INVENTION

An object of the invention is to provide a method and apparatus forcircuit pattern inspection capable of converting evaluation of the shapeof an edge, which is conventionally performed by view observation of animage into numbers, evaluating the edge shape quantitatively andpromptly with high precision, and specifying the cause of occurrence ofroughness systematically.

In the invention, a data process is directly performed on atwo-dimensional distribution image of secondary electrons or reflectedelectrons obtained by observation with a scanning microscope using acharged particle beam such as an electron beam, ionizing radiation, oran ion particle beam to obtain positions of edge points by a thresholdmethod while keeping the precision of the microscope, and deviations ofthe edge point positions from an approximation line, that is, edgeposition fluctuations are computed. A set of the edge positionfluctuations computed with respect to edge points belonging to one edgeexpresses a two-dimensional characteristic of the shape of edgeroughness. The computing operation is performed by using differentthresholds to obtain a plurality of sets of edge position fluctuations.By the sets, the shape of the three-dimensional edge roughness of theoriginal image is shown.

There is also provided a step of calculating and displaying a spatialfrequency distribution of the edge position fluctuations and thedependency on the threshold of the fluctuations. Consequently, a spacialperiod in which the intensity is particularly high, that is, the periodshowing the characteristic of the roughness can be found out.

By providing a step of calculating and displaying the dependency on thethreshold of the standard deviation of edge position fluctuations, thecase where the edge roughness is large around the surface and the casewhere the edge roughness is large in the bottom portion can bedistinguished from each other. In the former case, it can be estimatedthat the cause of occurrence of roughness is an atmosphere during apatterning process. In the latter case, it can be estimated the cause ismismatch of the patterned material with an underlayer.

There is also provided a step of calculating a correlation offluctuations in the right and left edge positions of one line, acoefficient of correlation, and dependency on the threshold of thecoefficient of correlation, and drawing viewgraphs based on thecalculation results. Consequently, whether the directions of roughnessof the right and left line pattern edges are (1) the same direction(FIG. 1), (2) opposite to each other (FIG. 2), or (3) at random, andwhether the types of the roughness changes in the depth direction or notcan be made clear.

FIGS. 1 and 2 show examples of the types of the roughness of edges inthe case where one line pattern exists in the vertical direction in animage. In the diagrams, reference numerals 1 and 3 denote left edges ofthe line, and 2 and 4 indicate right edges.

FIG. 1 shows a case where the width of the line is constant but the lineitself is wavy. FIG. 2 shows a case where the right and left edges ofthe line are synchronous but fluctuate in the opposite directionsdifferent from FIG. 1. When there is the tendency of (1), thecorrelation between the fluctuations in the right and left edgepositions is positive. When there is the tendency of (2), thecorrelation between the fluctuations in the right and left edgepositions is negative. When the right and left edges fluctuateindependently, there is no correlation. Concrete calculation andcriteria of determination of the coefficient of correlation will bedescribed hereinlater.

There are also provided a determining function, in which possible stepswhere roughness is considered to occur are selected based on thecalculation results, and a function of displaying them. By using asystem capable of transmitting a signal to a proper apparatus, a losscan be reduced by a conventional system in quick response to appearanceof a failure.

When the possibility that the cause of the edge roughness is theobserving apparatus itself is pointed out, to check the observingapparatus, a standard sample of the shape of a line is observed, anobservation position is moved in a direction parallel to the linepattern while acquiring image data, and images are added up. Althoughroughness which occurs at random in the obtained two-dimensional data isaveraged, distortion in an observed image remains without beingeliminated. By storing the distortion amount as data, distortion iseliminated in observation later, so that an image having a smaller errorcan be obtained.

According to the invention, there is provided a circuit patterninspection method of inspecting a pattern shape on the basis oftwo-dimensional distribution information of intensities of secondaryelectrons or reflected electrons obtained by observing a pattern formedon a substrate by a scanning microscope using a charged particle beam,characterized by including: a step of detecting a set of edge pointsindicative of positions of edges of the pattern in a two-dimensionalplane from the two-dimensional distribution information by a thresholdmethod; a step of obtaining an approximation line for the set of edgepoints belonging to the edges detected; and a step of obtaining an edgeroughness shape by calculating the difference between the set of theedge points and the approximation line.

According to the invention, there is also provided a circuit patterninspection method of inspecting a pattern shape on the basis oftwo-dimensional distribution information of intensities of secondaryelectrons or reflected electrons obtained by observing a pattern formedon a substrate by a scanning microscope using a charged particle beam,characterized by including: a step of detecting a set of edge pointsindicative of positions of line edges of the pattern in atwo-dimensional plane from the two-dimensional distribution information;a step of obtaining an approximation line for the set of edge pointsdetected for each line edge by least square; a step of obtaining an edgeroughness shape by calculating the difference between the set of theedge points belonging to each line edge and the approximation line; anda step of displaying correlation between edge roughness shapes ofdifferent line edges.

The invention is characterized in that, in the above configuration, aplurality of values are used as thresholds used for the thresholdmethod.

The invention is also characterized in that the above configurationfurther includes a step of calculating a spatial frequency distributionof the edge roughness shape obtained.

The invention is also characterized in that the above configurationfurther includes a step of obtaining the degree of the edge roughness bycalculating a standard deviation expressed by the square root of anaverage of root-mean-square values of the differences each between theset of the edge points derived with respect to the plurality ofthresholds and the approximation line.

The invention is also characterized in that the above configurationfurther includes a step of selecting a candidate of a process of forminga pattern of the substrate, which causes occurrence of roughness fromthe edge roughness shape obtained, and displaying the candidate.

Further, the invention provides a circuit pattern inspection methodincluding: a step of mounting a sample processed in a line pattern shapeat a predetermined pitch on a scanning microscope, observing the sample,and obtaining a two-dimensional intensity distribution of secondaryelectrons or reflected electrons; a step of calculating a shape ofroughness of an edge of the line pattern from the two-dimensionalintensity distribution; and a step of storing the edge roughness shapeobtained as image distortion information of the scanning electronmicroscope.

Further, the invention provides a circuit pattern inspection methodincluding: a step of mounting a sample processed in a line pattern shapeat a predetermined pitch on a scanning microscope, observing the sample,and obtaining a first two-dimensional intensity distribution ofsecondary electrons or reflected electrons; a step of moving anobservation position in the direction of an edge of the line patternonly by a predetermined length and obtaining a second two-dimensionalintensity distribution of secondary electrons or reflected electrons; astep of computing a sum of the first and second two-dimensionalintensity distributions; a step of calculating a shape of roughness ofan edge of the line pattern from the sum data; and a step of storing theedge roughness shape obtained as image distortion information. Further,according to the invention, the above circuit pattern inspection methodmay further include a step of calculating an image offset amount in thedirection perpendicular to an edge of a line pattern in an observationarea from the image distortion information obtained and correcting athird two-dimensional intensity distribution of secondary electrons orreflected electrons obtained as a result of observing an arbitrarysample or a pattern edge position obtained from the thirdtwo-dimensional intensity distribution.

Further, the invention provides a circuit pattern inspection apparatuscharacterized by including: a charged particle source; a chargedparticle optical system for irradiating a sample with a charged particlebeam emitted from the charged particle source through a condenser lens,a deflector, and an object lens, deflecting the beam, and performing thescan with the beam; a stage on which the sample is to be mounted; adetector for detecting intensity of a secondary electron or reflectedelectron emitted from the sample by irradiation of the charged particlebeam; a control system for controlling the deflection and scanning; andsignal processing means for obtaining an edge roughness shape and acharacteristic of the pattern on the basis of a threshold method from atwo-dimensional distribution of intensities of the secondary electronsor reflected electrons obtained.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of edges for explaining the first type ofline edge roughness.

FIG. 2 is a schematic diagram of edges for explaining the second type ofline edge roughness.

FIG. 3 is a conceptual diagram showing the configuration of an apparatusfor carrying out the invention.

FIG. 4 is a flowchart showing the procedure of a first embodiment of theinvention.

FIG. 5 is a schematic diagram of an observed image evaluated in thefirst embodiment of the invention.

FIG. 6 is a diagram showing line edges obtained in the first embodimentof the invention.

FIG. 7 is a diagram showing a spatial frequency distribution of lineedge roughness obtained in a second embodiment of the invention.

FIG. 8 is a diagram showing dependency (1) on a threshold of the degreeof roughness of a line edge obtained in a third embodiment of theinvention.

FIG. 9 is a diagram showing dependency (2) on a threshold of the degreeof roughness of a line edge obtained in the third embodiment of theinvention.

FIG. 10 is a diagram showing correlation between right edge roughnessand left edge roughness in one line obtained by a fourth embodiment ofthe invention.

FIG. 11 is a diagram showing dependency (1) on the threshold of acorrelation coefficient of right and left edge roughness in one lineobtained by the fourth embodiment of the invention.

FIG. 12 is a diagram showing dependency (2) on the threshold of acorrelation coefficient of the right and left edge roughness in one lineobtained by the fourth embodiment of the invention.

FIG. 13 is a flowchart for explaining the procedure of a fifthembodiment of the invention.

FIG. 14 is a flowchart for explaining a roughness analysis process inthe flow shown in FIG. 13.

FIG. 15 is a schematic diagram of an observed image which is evaluatedin the fifth embodiment of the invention.

FIG. 16 is a diagram showing threshold parameter dependence of thecorrelation coefficient of the right and left edge roughness in one lineobtained by the fifth embodiment of the invention.

FIG. 17 is a flowchart showing the procedure of a sixth embodiment ofthe invention.

FIG. 18 is a schematic diagram of a structure of a sample observed inthe sixth embodiment of the invention.

FIG. 19 is a schematic diagram of the observed image evaluated in thesixth embodiment of the invention.

FIG. 20 is a diagram showing an image distortion amount obtained by thesixth embodiment of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Embodiments of the invention will be described hereinbelow withreference to the drawings.

First Embodiment

A first embodiment of the invention will be described by referring toFIGS. 3 to 6. FIG. 3 is a schematic diagram showing the configuration ofan apparatus of the embodiment, FIG. 4 is a flowchart showing theprocedure of the embodiment, FIG. 5 is a schematic diagram showing animage formed from data used for evaluation, and FIG. 6 is a diagramshowing edges of a line pattern detected with a threshold parameter of0.5 from the data.

By using the apparatus shown in FIG. 3, an inspection is performed on apattern in accordance with the flow shown in FIG. 4.

First, as shown in a step 41, by performing an operation from a controlsystem 15 for a scanning electron microscope (SEM), a sample wafer 11mounted on a stage 12 in a column 5 is observed. An electron beam 7emitted from an electron emitter 6 of the SEM irradiates the samplewafer 11 on the stage 12 via a condenser lens 8, a deflector 9, and anobject lens 10, and a secondary electron 13 emitted from the samplewafer 11 is detected by an electron detector 14.

The structure of the sample wafer 11 has a line pattern of a resistformed by electron beam drawing on a silicon wafer. In the case wherethere is no record of measurement with respect to a spatial period ofedge roughness of the pattern or there is no particular request on thesize of an observation area, it is desirable to observe a sample waferat a magnification of 100,000 times to 300,000 times. In the example,the observation was made at a magnification of 200,000 times. The samplewafer 11 was mounted on the stage 12 so that the line pattern is almostperpendicular to the scan direction.

In step 42, scanning is performed a plurality of times, measurementresults of the intensities of the secondary electrons emitted from thepattern are added up, and an average value is calculated. In order toobtain an image with a low level of noise, the desirable number ofadding up of data is 64 times or more. In the example, the addingoperation was carried out 128 times.

A distribution of two-dimensional electron intensities obtained in sucha manner is data to be analyzed. The electron intensity distributiondata obtained is converted to shades of a gray scale so as to bedisplayed as an image on the screen of a terminal of a computer 16 foranalysis. FIG. 5 is a schematic diagram of the image.

The image data is composed of 512 pixels in the lateral direction and512 pixels in the vertical direction. In the case of detecting the shapeof edge roughness of an area which is long in the vertical direction,the pitch of scan lines corresponding to data in rows can be set to anintegral multiple of the pitch of pixels in the lateral direction. Forexample, an area having a width of 675 nm and a length of 2700 nm can bedisplayed on a screen of 512×512 pixels. In this example, an observationarea included in an image has a length of 675 nm and a width of 675 nm.One pixel corresponds to an area having about 1.318-square nm.Hereinbelow, the upper left of an image is set as the origin, a distanceto the right is expressed as x, and a distance downward is expressed asy. Numbers of pixels in the x and y directions are expressed as m and n,respectively. In reality, an image having shades according to theintensities of secondary electrons appears. In FIG. 5, an area in whichthe intensity of a secondary electron is particularly high, that is, anarea where an edge may exist is expressed as blank and an area having alow intensity of the secondary electron is hatched. The coordinatesshown in FIG. 5 indicate the numbers of pixels of an image. The electronbeam is stopped from being continuously emitted to the wafer, afterthat, the image data is transferred from the control system 15 to theneighboring computer 16. The step 42 is finished and the programadvances to step 43 where a program for analyzing a shape according tothe invention is executed.

The program performs averaging and smoothing operations on the data asdescribed below to thereby reduce noise. First, the data is divided intoa set of 512 intensities of secondary electrons arranged in a line, thatis, profiles. Each profile shows dependency on x of the intensity of thesecondary electron in the case where y is constant. The number ofprofiles is equal to the number of pixels in the y direction, that is,512 in total.

The data is subjected to noise reduction by the following procedure.First, an averaging parameter k₁ (natural number) and a smoothingparameter k₂ (odd number) are given. When k₁ is an even number,k₁′=k₁/2. When k₁ is an odd number, k₁′=(k₁−1)/2 and k₂′=(k₂−1)/2. Anaverage of k₁ profiles from the (N−k₁′)th profile is calculated and usedas the n-th profile averaged. Smoothing operation using a Hamming windowis performed on an area from pixel number m−k₂′ to pixel number m+k₂′ inthe averaged profile obtained in the preceding step, thereby newlyobtaining an m-th value smoothed. In the case of data in which one pixelcorresponds to a length from 0.8 nm to 2 nm, desirably, the averagingparameter k₁ is in a range from 4 to 11, and the smoothing parameter k₂is in a range from 3 to 11. If any of the parameters is below thecorresponding range, noise cannot be sufficiently reduced. If it is overthe range, edge roughness in a fine spatial period cannot be detected.In this example, k₁=k₂=7 was set.

Subsequently, to detect edges of a line, an area for retrieving edgepoints is input. First, with respect to the left edge, from the positionof an area 18 in FIG. 5, the pixel numbers in the x direction of theretrieval area are determined by eye-estimation as m=210 to 250 andentered. Similarly, with respect to the right edge, the pixel numberswere determined from the position of an area 19 by eye-estimation asm=280 to 320. The calculation areas can be designated by two ways: (1)entry of numerical values, and (2) entry on the screen of FIG. 5. Inthis example, numerical values were entered.

Subsequently, as shown in steps 44 to 47, the edge points are detected.The threshold parameter p for detection is used while being changed fromthe smallest value p₁ to the largest value p₂ of the set values p at aset pitch of Δp. In the example, with respect to the values of p₁=0.2,p₂=0.9, and Δp=0.1, the operation was performed on total 256 profileswhose pixel numbers n in the y direction are even numbers 2n′. Athreshold method used here is a generally known method in which, fromthe threshold parameter p and the highest value I_(max) and the lowestvalue I_(min) of the secondary electron intensity, the thresholdobtained by (I_(max)−I_(min))×p+I_(min) is calculated and points atwhich the intensity of the secondary electron becomes equal to thethreshold on the profiles are used as edges.

X coordinates at the right and left edge points detected are set asx_(R)(2n′) and x_(L)(2n′), respectively. The profile is a set (x, I(x))of numerical values I giving the secondary electron intensity at theposition to the x coordinate expressed by an integral multiple of thelength 1.318 nm of one pixel in the x direction. At the time ofcalculation, neighboring points are connected with straight lines, andthe intersections between the polygonal line and the threshold value areobtained. The y coordinate of the edge point obtained in such a manneris 2n′×1.318 (unit: nm).

By the above process, for one value of p, 256 (x_(L), Y) coordinates canbe derived with respect to the left edge. Similarly, a set of 256 pointscan be obtained with respect to the right edge. A process of setting 0.2as the value of p (step 44), detecting an edge, and increasing the valuep by 0.1 is repeated until the value p becomes 0.9 (steps 45 to 47). Asan example, FIG. 6 shows a set of edge points obtained in the case wherep=0.5.

As shown in step 48, total 512 points of the right and left edges areapproximated by using least square. Generally, it is possible toapproximate the edge points with arbitrary functions. In this case, weuse a set of parallel straight lines x=ay+b and x=ay+b+w.

In step 49, with respect to a profile obtained when the y coordinate isan even number 2n′, the difference between the x coordinate x_(L)(2n′)at the left edge point and the intersection of the approximate straightline and the profile, that is, the x coordinate ax2n′+b at theapproximate point is calculated as an edge point fluctuationΔx_(L)(2n′). The calculation is similarly performed with respect to theprofiles from n′=1 to n′=256, thereby obtaining fluctuations at the 256left edge points. At the time of calculation, the positions of thepoints are expressed by x and y in the unit of length of nm. However,the process may be performed by expressing the positions of the pointsby pixel numbers m and n. In the latter case, n is a positive integer,so that a storage capacity to be used can be small. Similar calculationis also executed with respect to the right edges, thereby obtaining 256right edge point fluctuations. In such a manner, the set of edgeposition fluctuations (Δx_(L)(2n′), 2n′) (Δx_(R)(2n′), 2n′) (where,n′=1, 2, . . . , and 256) indicative of the shape of edge roughness canbe obtained. The program also calculates the values for every threshold.The results of the calculations are stored in the storage area in acomputer.

As a result, the shape of edge roughness can be taken out as digitaldata from a microphotograph expressed in shades of the gray scale andcan be displayed as a set of points on a graph. Consequently, the edgeshape can be display more clearly. An analysis is further conducted byusing the data, so that the pattern shape can be analyzed as well.

Second Embodiment

A second embodiment of the invention will be described by referring toFIGS. 5 and 7.

By the method described in the first embodiment, edge positions aredetected from the image data of a resist pattern shown in FIG. 5 and,further, data indicative of an edge roughness shape is obtained asfluctuations in the edge positions.

Subsequently, a set of edge position fluctuation data (Δx_(L)(2n′), 2n′)(or a set of (Δx_(R)(2n′), 2n′)) obtained at each threshold is regardedas a summation of periodical functions in the y direction and adistribution of the periods is obtained. Specifically, Fourier transformis performed on a data series {Δx_(L)(2), Δx_(L)(4), Δx_(L)(6),Δx_(L)(8), . . . } to obtain the absolute value of a Fourier coefficientfor a spatial frequency (f) in the y direction, that is, the intensityA(f).

FIG. 7 shows an example of the frequency distribution derived as aresult. This is the result of the Fourier transform performed on theleft edge of the line illustrated in FIG. 6. The spatial frequency (f)on the lateral axis denotes a ratio of the image area length 675 nm tothe corresponding spatial period. For example, f=10 corresponds to aspace period of 675 nm/10, that is, 67.5 nm.

Next, the characteristic spatial frequency in the frequency distributionis extracted by the following procedure. The intensity A(f) in the areaof 15<f<128 is approximated by a function A₀×1/f by using least square,and the function A₀×1/f for which a fitting parameter A₀ obtained issubstituted is plotted onto the graph in all of areas where f<128. Thecurve expressed by a thick solid line in FIG. 7 is an approximated curvederived in such a manner. A(f) as an actually measured value in apreliminarily designated area of (f) is compared with the approximationvalue A₀×1/f. The value (f) at which A(f) is larger than A₀×1/f ispicked up. In the example, the designated area was set as 3<f<20.

The analysis was performed on the right and left edge roughness at allthe threshold parameters. From the analysis, it was found that thecomponents of the spatial frequency of f=5 and f=7 largely contribute tothe roughness.

As one of quantities characterizing the edge roughness obtained in sucha manner, the space period which can be said as characteristic roughnesscan be extracted. As described above, as a result of inspecting thepattern shown in FIG. 5, numerical values f=5 and f=7 were obtained.When the roughness at the constant frequencies are observed irrespectiveof the thresholds, considered are a case where a pattern is formeddistorted over a full range from the bottom to the surface area and acase where the frequency components are distortion of an observed image.In the former case, the cause of the edge roughness is resist exposureequipment. In the latter case, the cause is the observing apparatus. Asdescribed above, by making the inspection, candidates of processes asthe cause of occurrence of roughness can be selected.

Third Embodiment

A third embodiment of the invention will be described by referring toFIGS. 5, 8, and 9.

By the method described in the first embodiment, edge positions aredetected from image data of a resist pattern shown in FIG. 5 and,further, data indicative of the shape of edge roughness is obtained asfluctuations in the edge positions.

Next, from the edge position fluctuation data obtained at thethresholds, an amount expressed by the following Equation 1, that is, astandard deviation in a fluctuation distribution is calculated, and avalue 3σ which is three times as large as the standard deviation isdefined as the degree of edge roughness.

$\begin{matrix}{\sigma = \sqrt{\frac{\sum\limits_{n^{\prime}}^{\;}\;{\Delta\;{x_{k}\left( {2n^{\prime}} \right)}}}{256}}} & \left( {{Equation}\mspace{20mu} 1} \right)\end{matrix}$

where an index k is equal to L or R. This calculation is executed ateach threshold, thereby obtaining the relation between the thresholdparameter p and the degree of roughness 3σ with respect to one lineedge. FIG. 8 shows the result of the calculation executed on the exampleillustrated in the schematic diagram of FIG. 5. It is understood thatthe degree of roughness hardly depends on the threshold but is almostconstant.

The graph of the dependency on the threshold parameter p of the degree3σ of roughness can be also quantitatively analyzed as follows. Thegraph of the threshold parameter to 3σ is approximated by least squarewith a linear function y=ax+b where y is the value of 3σ (unit: nm) andx is the threshold parameter. The value of the obtained fittingparameter (a) is compared with a preset value α₁. When a>α₁, it isdetermined that 3σ increases as p increases, in other words, roughnessis large around the surface. The value a is also compared with a presetvalue α₂. When a<α₂, it is determined that 3σ decreases as p increases,in other words, roughness is large around the bottom of the resistpattern.

From the results of inspections on line patterns of conventionalresists, 4 and −4 are standard values as set values of α₁ and α₂,respectively. The observer can set other values.

When the method is applied to the result illustrated in FIG. 8, (a) isequal to 0.02. It is therefore understood that the degree of theroughness is almost constant from the bottom of a pattern to a portionaround the surface.

An inspection was also conducted on an image obtained by observing thepattern of another resist, and dependency on the threshold as shown inFIG. 9 was obtained. In this graph, the value (a) is 6.62 and it isdetermined that the roughness is large around the surface. Since theresist is a chemically amplified negative resist, it is pointed out thatacids on the surface of the resist are possibly deactivated in an alkaliatmosphere. The concentration of amine in the atmosphere was measuredand it was confirmed that the concentration of amine was higher thanbefore. In such a manner, from the dependency on the threshold of thedegree of roughness, the candidate of the process causing roughness canbe selected.

Fourth Embodiment

A fourth example of the invention will be described by referring to FIG.5 and FIGS. 10 to 12.

By the method described in the first embodiment, edge positions aredetected from image data of the resist pattern shown in FIG. 5 and,further, data indicative of an edge roughness shape is obtained asfluctuations in the edge positions.

From a set of edge position fluctuation data (Δx_(L)(2n′), 2n′) and aset of (Δx_(R)(2n′), 2n′) obtained at each threshold, the fluctuationsin the position of the left edge and those in the position of the rightedge having the same y coordinate are combined, thereby obtaining 256points ((Δx_(L)(2n′), Δx_(R)(2n′)). A graph is made from the points asshown in FIG. 10. This is the case where p=0.5.

From the result, it is understood that roughness of the right and leftedges has a positive correlation. Based on the data, a coefficient ρ ofcorrelation of the right and left edge position fluctuations when p=0.5is calculated according to Equation 2. The numerator of the right sideof Equation 2 is the amount expressed by Equation 3.

$\begin{matrix}{\rho = \frac{{Cov}\left( {L,R} \right)}{\sigma_{L} \cdot \sigma_{R}}} & \left( {{Equation}\mspace{20mu} 2} \right) \\{{{Cov}\left( {L,R} \right)} = {\frac{1}{256}{\sum\limits_{n^{\prime} = 1}^{256}\;\left\{ {\Delta\;{{x_{L}\left( {2n^{\prime}} \right)} \cdot \Delta}\;{x_{R}\left( {2n^{\prime}} \right)}} \right\}}}} & \left( {{Equation}\mspace{20mu} 3} \right)\end{matrix}$σ_(L) and σ_(R) are standard deviations in the distributions offluctuations of the left edge position and right edge position,respectively, and each of which corresponds to ⅓ of the degree ofroughness. ρ is calculated as 0.64.

From the value ρ, the type of roughness can be classified as follows.The value ρ is compared with a preset reference value ρ_(th) of theabsolute value of ρ, and if ρ>ρ_(th), the type of FIG. 1 is determined.If ρ<−ρ_(th), the type of FIG. 2 is determined. If none of the cases, itis determined that there is no correlation. In the example, p_(th) isset as 0.4. Although the value is a standard value, the observer can useanother value. It is understood that the line pattern illustrated inFIG. 5 has roughness of the type of FIG. 1 when p=0.5.

With respect to the line pattern illustrated in FIG. 5, further, whilechanging the value p from 0.2 to 0.9 at intervals of 0.1, the value of ρwas calculated. The result is shown in FIG. 11. It is found thatdependency of ρ on p is small.

The graph of dependency of ρ on p can be also analyzed quantitatively asfollows. The graph of the threshold p with respect to ρ is approximatedwith the linear function of y=cx+d by least square. In this case, y isthe value ρ, and x is the threshold p.

The value of the obtained fitting parameter c is compared with a presetvalue γ₁. When c>γ₁, ρ increases as p increases. That is, it isdetermined that the correlation between the right and left edgefluctuations is higher around the surface. When the value c is comparedwith a preset value γ₂, if c<γ₂, ρ decreases as p increases. That is, itis determined that correlation between the right and left edgefluctuations is larger around the bottom of the resist pattern.

From the result of the inspections on the line pattern of the resist,conventionally, as the set values γ₁ and γ₂, 0.4 and −0.4 are standardvalues, respectively. Although the observer can set other values, in theexample, the inspection was conducted by using the standard values.

When the method is applied to the result shown in FIG. 11, c becomesequal to 0.15, and it is understood that the correlation of the rightand left edge fluctuations is constant from the bottom to the top of thepattern.

An inspection was also conducted on an image obtained by observing thepattern of another resist, and dependency on the threshold shown in FIG.12 was derived. In the graph, the value c is 0.57 and it is understoodthat the tendency that the right and left edges fluctuate togetherbecomes stronger as the distance to the surface becomes shorter. Sincethere is no correlation of fluctuations of the right and left edges inthe bottom part and the right and left edges fluctuate with the widthbeing kept constant around the surface, it is estimated that a patternonce formed is distorted in the time of development or baking after thedevelopment due to its insufficient physical strength. As describedabove, from the dependency on the threshold of ρ, candidates of aprocess causing the roughness can be selected.

Fifth Embodiment

A fifth example of the invention will be described by referring to FIGS.1 to 3, FIGS. 5 to 8, FIGS. 10, 11, 13, and 14.

Firs to fall, the outline of the procedure will be described withreference to FIGS. 13 and 14. FIG. 14 shows the details of a part ofstep 139 in the flow of FIG. 13.

By a procedure similar to that of the first embodiment, first, a linepattern is observed with a scanning microscope and data is captured(steps 131 and 132). Acquired two-dimensional data is subjected to noisereduction by the method described in the first embodiment (step 133),and the shape of edge roughness is obtained by using a standard value p(usually, 0.5) (step 134). Further, from the data of the edge roughnessshape, with respect to all the edges in the image data, the degree (3σ)of roughness given by Equation 1 is calculated (step 135).

The program advances to step 136 and whether a wafer is good or not isdetermined. Only in the case where 3σ of all of the edges measured issmaller than a reference value, a wafer with a pattern to be observed isdetermined as good and passed to the following process. It is alsopossible to select whether the shape analysis in step 139 and subsequentsteps is performed or not irrespective of the result of thedetermination (steps 137 and 138). If NO, the inspection on the wafer tobe observed is finished. A good wafer is passed to the next step and anon-conforming wafer is taken out from the lot.

In the case of making the shape analysis, the program advances to step139 where a line to be observed is selected from two-dimensional data ofwhich noise has been reduced, and edge detection is sequentiallyperformed by using a plurality of thresholds as described in the firstembodiment to obtain data of an edge roughness shape with respect toeach of the thresholds.

After the data is obtained, the data is processed according to the flowshown in FIG. 14. The data process includes three kinds of inspectionsfor showing the characteristic of the edge shape and any of theinspections desired is selected (step 147). Although it is desirable toselect all of the processes to obtain a result with high reliability,two or even one of the processes may be executed to shorten theexecution time. The details of steps 148 to 150 will be describedhereinbelow.

The first process is calculation of the space frequency showing thecharacteristic of the edge roughness shape. The spatial frequencydistribution is calculated by a method described in the secondembodiment and, after that, characteristic spatial frequencies common tothe spatial frequency distribution of the edge roughness shapes at allthe thresholds are picked up (step 148).

The second process is calculation of the dependency on the threshold ofthe degree of roughness. The dependency is calculated by the methoddescribed in the third embodiment (step 149).

The third process is calculation of a graph indicative of thecorrelation between right and left edge fluctuations belonging to oneline with respect to thresholds, and calculation of dependency on thethreshold of the correlation coefficient of the right and left edgefluctuations. They are calculated by the method described in the fourthembodiment (steps 150 and 151).

Analysis results of the items are displayed (step 152). After that, asshown in step 140 in FIG. 13, whether the roughness causing process isspecified automatically or not is selected. In the case of NO, ifnecessary, the above result is examined by the observer and theinspection on the wafer to be observed is finished. The wafer isprocessed according to the result of the determination of conformity(step 144). In the case of automatically specifying the roughnesscausing process, by checking the result with the reference in step 141,the program determines whether or not there is the possibility that anyof the pattern generating processes causes the roughness and outputs theresult. Further, in the case where the control on the fabricatingapparatus in the pattern generating process is performed by theinspection apparatus, as shown in steps 142 and 143, a signal is sent tothe fabricating apparatus in accordance with the result, the inspectionon the wafer to be observed is finished, and the wafer is processedaccording to the determination of conformity (steps 144 to 146). Theinspection performed in the example will be concretely describedhereinbelow.

In the example, in a manner similar to the first embodiment, an image ofa line pattern of an electron beam resist shown in the schematic view ofFIG. 5 is inspected by using the apparatus shown in FIG. 3. The resistused for generating the pattern is a negative type.

First, two-dimensional data indicative of an image is processed by usingthe method and parameters described in the first embodiment, and edgeroughness shapes of the right and left edges at the threshold p=0.5 areobtained. The shapes are as shown in FIG. 6. Subsequently, the degree ofthe right and left edge roughness is calculated by using the data anddisplayed together with the image. The sample to be observed issubjected to the determination of conformity and determined as a gooditem. The reference value of the roughness of the conforming item in theinspection is set to 6 nm. In the case where the sample is determined asa defective, an alarm sound is generated and the numerical values ofroughness larger than the reference value are displayed in red in animage. The numerical values equal to or smaller than the reference valueare displayed in white or black.

Although the sample was determined as good, the analysis on the shape ofroughness was subsequently performed. First, by using the method andparameters described in the second embodiment, the spatial frequency wasanalyzed, the spatial frequency distribution at the threshold p=0.2 to0.9 was obtained and, as characteristic frequencies common to thedistributions, f=5 and 7 were found out. FIG. 7 shows the case wherep=0.5.

By using the method and parameters described in the third embodiment,the dependency on the threshold p of the degree 3σ of roughness wascalculated. A graph shown in FIG. 8 was displayed and a result such thatthe degree 3σ of roughness hardly depends on p was obtained.

Subsequently, by using the method and parameters described in the fourthembodiment, the correlation of the right and left edge roughness shapeswas calculated as a coefficient of correlation, and the dependency onthe threshold p of the coefficient of correlation was calculated. As aresult, graphs shown in FIGS. 10 and 11 were obtained and it was foundthat the coefficient of correlation is positive and larger than thereference value, that is, the fluctuations are of the type shown in FIG.1, and the tendency does not depend on the threshold p.

The observer displayed the results and operated the automaticdetermining function of determining the roughness causing process. Theprocedure of narrowing candidates of the roughness causing process of aresist of a general automatic determining program will be describedherein below. For setting of values such as α₁ and α₂ used for thedetermining methods, setting of a reference used to narrow thecandidates, and setting of exceptions, not only the general referencevalues used in the example but also data accumulated by the user arehelpful. With them, roughness of a pattern of something other than theresist can be also inspected. In the example, a memory device isprovided for the computer in order to accumulate data.

First, as candidates of the cause of roughness, (1) chemical property ofthe resist, (2) exposure equipment, (3) developer, (4) atmosphere, (5)the surface of the substrate, (6) underlayer pattern, and (7) observingapparatus can be mentioned.

Concretely, (2) indicates edge roughness of a reticle pattern or aposition or strong fluctuation of a beam at the time of drawing. (3)indicates distortion of a whole line due to swelling caused by mismatchof the density of a developer or an eddy of the developer. (4) indicateserosion of the surface of a pattern by amine or acids in the atmosphere.(5) indicates footing due to the chemical nature such as insufficientprocessing on the surface of the substrate. (6) indicates unevenness ofreflectance due to a lower layer pattern. (7) indicates distortion of animage due to electric noise or vibration.

Among the inspection items, in the calculation of the first frequencydistribution, if p=0.5 and a characteristic frequency is not seen, thereis the possibility that (1), (2), (4), and (5) out of the above causesare the causes, so that (3), (6), and (7) are eliminated. If acharacteristic frequency is seen, the possibility of (5) is eliminated.If the frequency is 20 or higher, (7) is eliminated. When thecharacteristic frequency is converted to a period which is 0.5 μm orless, (3) is eliminated. When no characteristic frequency is seen atp=0.2 and 0.3 but is seen at p=0.8 and 0.9, (3) is possible. Morespecifically, it is considered that the physical strength of a resist isweak and an area around the surface is distorted by an external forcegenerated after the pattern is formed, such as an eddy of the developer.

From the dependency on the threshold of the degree of roughness as thesecond inspection item, the following is determined. When it isdetermined that roughness is larger around the surface from the graphindicating the degree of edge roughness at p=0.2 to 0.9 by using themethod described in the third embodiment, the causes (1) and (4) arepossible but the others are eliminated. On the other hand, when it isdetermined that roughness is larger around the bottom of the pattern,there are possibility of (1) and (5).

As the third inspection item, when there is the correlation of right andleft edge roughness at p=0.5 and the type shown in FIG. 1 is determined,there are the possibilities of (2), (3), and (7). In the case where thetype shown in FIG. 2 is determined, there are the possibilities of (2)and (6). When the dependency on the threshold of the coefficient ofcorrelation is calculated and, as a result, the correlation is largeonly around the surface, in addition to the roughness of the type ofFIGS. 1 or 2, the cause (5) is possible. Consequently, it is consideredthat roughness having no correlation between right and left edgeroughness occurs around the bottom portion, so that roughness havinglarge correlation between the right and left edge roughness (of the typeof FIGS. 1 or 2) is inconspicuous in the bottom portion. On the otherhand, when it is determined that the correlation is high only in thebottom portion, in addition to the roughness of the type of FIGS. 1 or2, it is also considered that a portion around the surface is largelyeroded due to the roughness having no correlation between right and leftedge roughness due to the cause of (4).

According to the determination criteria, the cause of the edge roughnessshown in FIG. 5 was determined as (2) or (7). The observed wafer wassent as a conforming item to the following process, and the inspectionwas once finished.

Next, a resist pattern formed by different exposure equipment wasinspected, the same result as the above was derived. Consequently, theobserver determined that there is the higher possibility that (7) is thecause than (2), and the scanning electron microscope was inspected. Itwas found that the screen of the observing apparatus is distorted due toan influence of the magnetic field generated from a peripheral device.By thoroughly performing shielding against the magnetic field, therebecame no distortion, and measurement of higher precision could beperformed.

Sixth Embodiment

A sixth embodiment of the invention will now be described by referringto FIG. 3 and FIGS. 15 and 16. FIG. 15 is a concept diagram showing animage of data used for evaluation. FIG. 16 is a graph showing thecorrelation of right and left edge position fluctuations of a linepattern observed.

The pattern shape was evaluated and determined by using the apparatusshown in FIG. 3 in accordance with the same flow as that of the fifthembodiment.

First, by performing an operation from the control system 15 of ascanning electron microscope having a length measuring function, a linepattern of a positive type ArF resist formed on a silicon wafer isobserved by ArF lithography on the sample wafer 11. For the purpose ofobserving edge roughness having a large space period, the magnificationis desirably 100,000 times or less. In the example, the observation wasmade at the magnification of 100,000 times. The line pattern to beobserved is mounted in the direction almost perpendicular to the scandirection. The observation area has a length of 1.35 μm in the directionperpendicular to the line pattern and a length of 5.40 μm in thedirection parallel to the line pattern, and the distance betweenneighboring scan lines is 10.55 nm. When the purpose is to observe thepresence or absence of fluctuation in edge position of a large spaceperiod regarding a narrow line pattern, it is desirable to set theaspect ratio of the observation area to 2:1 or higher. Since the lengthin the vertical direction of the area to be observed was 6 μm in theexample, 4:1 was set. After scanning 64 times, the measurement resultsof intensity of secondary electrons emitted from the pattern were addedup, the average value was used as shades of the gray scale, and theshades were displayed as an image on the screen of the control system15.

FIG. 15 is a schematic diagram of an image appeared on the screen. Theimage data is constructed by 512 pixels in the lateral direction and 512pixels in the vertical direction. It is assumed that the upper leftpoint of the image is the origin, the distance to the right is expressedas (x), and the distance to the left is expressed as (y). The number ofeach of pixels in the (x) direction is expressed as (m), and the numberof each of pixels in the (y) direction is expressed as (n). The area ofone pixel has an area having a length of 2.637 nm in the x direction anda length of 10.55 nm in the y direction. In reality, an image havingshades according to the intensities of secondary electrons appears. InFIG. 15, areas where the intensity of secondary electrons is high, thatis, an edge can exist are expressed in white, and areas in which theintensity of secondary electrons is low are hatched. The coordinatesshown in FIG. 15 express the image pixel numbers.

After stopping irradiation of the electron beam to the wafer, the imagedata was transferred from the control system 15 to the computer 16adjacent to the control system 15. A program for conducting aninspection according to the invention was executed from a terminal ofthe computer 16. The program processed an image file converted to thenumerical value data of 512×512 pixels by using the threshold methoddescribed in the first embodiment, and the coordinates of edge points oftotal four edges of two lines existing in the image were detected. Inconsideration of the balance between noise reduction and accuracy, theaveraging parameter was set to 4, and the smoothing parameter was set to3. Calculation was executed on all of profiles, that is, 512 profiles,and the threshold p was set to 0.5. An entered edge retrieval area wasset as follows. By eye estimation from the position of an area 20, thearea of the left edge of the first line was determined from m=170 to200. The right edge of the first line was determined from m=230 to 270on the basis of the position of an area 21. The left edge of the secondline was determined on the basis of the position of an area 22 as m=340to 380. The right edge of the second line was determined on the basis ofthe position of an area 23 as m=410 to 450.

A set of points indicative of the four edges was approximated by leastsquare with four straight lines x=ay+b₁, x=ay+b₁+w₁, x=ay+b₂, andx=ay+b₂+w₂ which are parallel to each other, and the edge pointfluctuations were calculated by the same method as that of the firstembodiment. For example, a fluctuation in the left edge point of thefirst line obtained with respect to a profile whose y coordinate is aninteger (n) is described as Δx_(1L)(n) and a fluctuation in the rightedge point is described as Δx_(1R)(n). Fluctuations on all of profileshaving n of 1 to 512 were calculated.

Next, when whether the sample is good or not was determined, the all ofthe line edge roughness degree were larger than 6 nm and an alarm soundwas generated. The shape analysis was further conducted to see the causeof this large roughness, and only the first and third inspection itemsdescribed in the fifth embodiment were conducted.

The spatial frequency analysis as the first inspection item wasperformed on the total four edges of both right and left edges of thefirst and second lines. The derived graph was displayed on the screen ofthe computer 16. Subsequently, by a method similar to that in the firstembodiment, the intensity A(f) in the area of 15<f<256 was approximatedby the function A₀×1/f, and the function A₀×1/f for which the obtainedfitting parameter A₀ was substituted was plotted on the graph. Aftercalculating all the edges, the intensity of the actual measurement valuewas higher than the approximation value in any cases where f=6, 7, 13,14, 19, 20, 27, and 34. It means that the line width changes inpredetermined cycles, and the cycle is about 1/7 to ⅙ of the length 5.40μm of the image subjected to the data process.

Next, the third inspection was performed, specifically, the coefficientof correlation of sets of the right and left edge points of one line wascalculated. At any of the values p, the coefficient of correlation ofthe first line lies in the range of ±0.12 of −0.52, and the coefficientof correlation of the second line lies in the range of ±0.14 of −0.45.It was found that there is a strong negative correlation. FIG. 16 showsa graph of the correlation between the right and left edges in the firstline when p is 0.5.

The function of determining the roughness causing process was executedhere. A warning of an abnormal appearance of a pattern in the underlayeras the cause (6) of roughness described in the fifth embodiment wasdisplayed and an instruction to temporarily stop the lithography processperformed on the substrate and make a check was given. The details ofthe warning were displayed, and the possibility that periodic patternsexist in the underlayer substrate at a pitch of 0.7 to 0.9 μm and causea unevenness of reflectance was pointed out.

According to the warning, a signal is sent from the computer 16 to alithography system 17 to stop the lithography process, the processesbefore the lithography were also temporarily stopped, and the history ofthe substrate was referred to. It was recognized that metal linepatterns exist in the substrate in the direction perpendicular to theline pattern observed, and the pitch of the metal line patterns was 0.8μm. It is estimated that, in an area on the metal line patterns,antireflection is imperfect, and the line pattern of the resist wasconsequently narrowed. Based on the estimation, antireflection wasthoroughly performed. After that, such a phenomenon stopped appearing,and the yield was improved. By temporarily stopping the processes inresponse to the warning, the number of wafers going back to fabricationof an antireflection film could be minimized.

Seventh Embodiment

A seventh embodiment of the invention will be described by referring toFIG. 3 and FIGS. 17 to 20. FIG. 17 is a flowchart for acquiring imagedistortion data. FIG. 18 is a schematic cross section of a sample used.FIG. 19 is a schematic diagram showing the screen of a microscopeshowing arrangement of the sample at the time of observation. FIG. 20 isa graph showing an image distortion amount obtained.

Detection of distortion and acquisition of data for correction wereperformed by using the apparatus of FIG. 3 in accordance with the flowof FIG. 17.

First, an operation was performed from the control system 15 of thescanning electron microscope having the length measuring function, and astandard sample made of silicon mounted on the stage 12 of the electronmicroscope was observed (step 171). The cross section of the structureof the sample is shown in FIG. 18. FIG. 19 is a diagram of the structureobserved from above, having a line and space shape. Since themagnification of 100,000 times or higher is desired for measuring edgeroughness of a line pattern and it is necessary to observe the edges ofat least two line patterns by the method, the pitch of theline-and-space pattern formed on the standard sample is desirably 0.5 μmor less. The ratio of the line width to the space width is desirably 1or less. In the example, a sample having a pitch of 0.24 μm and the linewidth of 0.10 μm was used and observed at the magnification of 200,000times. The area to be observed was a square area of 675×675 nm. Theresult of observation, that is, the intensity distribution of detectedsecondary electrons, was displayed as shades of the gray scale on pixelsin corresponding portions. The observed area is displayed as an image of512×512 pixels.

As an initial position, the sample was mounted so that the center of aspace part 25 between two lines 24 almost coincides with a vertical axis26 indicative of the center of the observation area. The edge directionof the line pattern was so arranged to be in parallel with the verticalaxis 26 by view observation.

Subsequently, a data accumulating program for detecting distortion wasexecuted.

First, a storage area for taking in image data in the control system 15in the scanning electron microscope was initialized to set all values to“0”. The following first and second procedures were performed repeatedly(corresponding to an operation of performing steps 172 and 174, andreturning again to step 171).

First, scanning was performed eight times with the scanning electronmicroscope, the intensities of secondary electrons emitted from thesample were added up, and the average value was calculated and added tothe memory area of the control system (step 172). Second, theirradiation of an electron beam was stopped and a check is made to seewhether or not the scan has reached the repetition number of times whichhas been set (step 173). If “Yes”, the program advances to the followingstep 175. If “No”, the scan position is moved upward in the screen by anamount of eight pixels, that is, 10.55 nm (step 174). The number ofrepetition times was set 128. It took about 40 seconds to integrate 128average image data of eight scans. Desirably, the number of scans in thefirst procedure is at least four in order to reduce noise. It is alsodesirable that observation area of the first time and that of the lasttime are not overlapped with each other, so that the product between themovement distance in the second procedure and the number of times forrepeating the first and second procedures is preferably set to be equalto or larger than the length in the vertical direction of the area whichcan be observed at a time. In the following, it is assumed that theupper left point of an image is set as an origin, the distance to theright side is (x), and the distance to the below is (y). The numbers ofpixels in the x and y directions are expressed by (m) and (n),respectively.

The above process was finished and data of the secondary electronintensity distribution of 512×512 pixels stored in the memory area ofthe control system 15 was divided by the number of repeating times,thereby obtaining an average value per observation. The program advancesto step 175. The obtained 512×512 two-dimensional data array is dealt asdata of one image, and noise was reduced by the method described in thefirst embodiment (step 175). The edge detection and calculation of anapproximation line were performed by the threshold method (step 176).The detection was performed on the right and left edges of the first andsecond lines in an image. Each of the averaging parameter and thesmoothing parameter was set to 11. 0.5 was used as the thresholdparameter. Detection was performed on all the profiles and 512 edgepoints were calculated per edge. From the data, a set of edge pointfluctuations was obtained (step 177). Further, as a reference, thedegree of edge roughness, that is, 3σ was calculated by Expression 1.The program may advance to step 178 without calculating 3σ.

In the example, the purpose was to detect image distortions caused by aninfluence of an apparatus having a power source disposed near thescanning microscope or a power supply cable. The image distortionsappear in an area where the spatial frequency is 20 or lower in animage. When the spatial frequency of 20 is converted to a space period,about 25 pixels are derived. Consequently, numerical values equal to orlower than 25 have to be used as the averaging parameter and thesmoothing parameter. The larger the parameters are, the more the noisecan be reduced. However, when the parameters are too large, an image isaveraged too much as a whole. In consideration of the above, it isdesirable to use a value from 7 to 15.

As a result of the processes, data of four edges were obtained. The dataof one edge is constructed by position coordinates of the 512 edgepoints. The edges are not actually existing edges but are obtained byaveraging actual edge data in the y direction by the above method.Therefore, roughness which occurs at random in the lines observed iseliminated by the averaging.

However, in reality, the degree 3σ of roughness of the edge data wasabout 3 to 4 nm. The value is large as a noise, and there is thepossibility that the microscope image itself is distorted. From thedata, the coefficient of correlation of the right and left edgeroughness was computed by the method described in the fourth embodiment,and 0.68 was obtained. The coefficient of correlation of the right andleft edge roughness of the second line was also high as 0.55.

The coefficient of correlation between edges belonging to differentlines were computed. To be specific, the combinations are (1) the leftedges of the first and second lines, (2) the left edge of the first lineand the right edge of the second line, (3) the right edge of the firstline and the left edge of the second line, and (4) the right edges ofthe first and second lines. All the coefficients of correlation computedwere equal to or higher than 0.5. It means that the whole image isdistorted but is seen like a part of the profiles is parallel-translatedin the x direction. Consequently, it was determined in step 179 that theimage has to be corrected.

Next, the four edge roughness was averaged every profile number and theresultant was used as an image distortion of the microscope itself. FIG.20 shows a graph of an image distortion amount Δx(n) with respect to anobtained line profile number (n). It is also possible to regard theroughness of an edge close to the center as an image distortion amountwithout averaging data of the four edges. The data of the imagedistortion amount obtained was recorded in a file (step 180).

An arbitrary sample was observed at the same magnification, and theimage distortion of an obtained profile of the intensity of thesecondary electron was corrected with an offset of −Δx (n). When thedistortion amount is large, by dividing the offset amount −Δx(n) of eachprofile by scan speed to calculate offset time and deviating the scanstart timing of each profile by the offset time, similar effects areobtained.

In the case of making observation at different observationmagnifications, a file of image distortion data Δx(n) at each of themagnifications is generated by the above procedure and, by using thefile, an image distortion was corrected by the above method.

Consequently, without thoroughly correcting hardware as didconventionally, the image distortion of the scanning electron microscopeis eliminated by a cheap and easy method, and an inspection of highprecision can be conducted.

Although observation of a two-dimensional distribution of secondaryelectrons by a scanning microscope using electron beams has beendescribed as an object in all of the foregoing embodiment, the inventioncan be also applied to a case using a two-dimensional distribution ofparticles such as reflected electrons which are emitted secondarily froma sample. The invention can be also applied to cases of observation by ascanning microscope using a charged particle beam such as an ionparticle beam or ionizing radiation or, further, light.

As described above, according to the invention, by observing a finepattern with the scanning microscope, that is, by a non-destructiveinspection, the three-dimensional shape of a pattern edge can beexpressed in numerical value data. Degree of roughness in the directionalong a line, a wavy state of a line, and the difference in theroughness shape between a bottom portion and a portion around thesurface of a pattern can be quantitatively expressed.

Further, by analyzing the results, candidates of processes as a maincause of roughness are selected, and the fabricating process of asemiconductor device or a micromachine can be controlled. An imagedistortion of the microscope itself used for observation can be alsoextracted and eliminated from an arbitrary image by a simple, cheapmethod.

According to the invention, the method and apparatus for circuit patterninspection capable of converting the evaluation of characteristics ofedge shape, which is conventionally visually observed, into values,performing analysis quantitatively and promptly with high precision, andspecifying the cause of occurrence of roughness systematically can berealized. Further, by using the method and apparatus to control thefabricating process or fabricating apparatus causing the roughness, asuper minute patterning process is managed, so that improvements inyield and throughput can be expected.

1. A system for measuring a pattern on a sample, comprising: a dataprocessing system that processes a set of two-dimensional distributiondata of intensities from the sample, to calculate; a set of edge pointsindicative of position of edges of said pattern in a two-dimensionalplane from said two-dimensional distribution data; an approximation edgeindicative of the edge of the pattern; an edge fluctuation data bycalculating a difference between the set of edge points and saidapproximation edge; and a correlation coefficient between a firstportion of the edge fluctuation data and a second portion of the edgefluctuation data.
 2. The system according to claim 1 wherein: saidpattern is a line pattern defined by a set of at least two edge points;and the data processing system calculates the correlation coefficientbetween the first portion of the edge fluctuation data for one side ofthe line pattern and the second portion of the edge fluctuation data foran opposite side of the line pattern.
 3. The system according to claim2, comprising: a memory device that stores a table of candidatecoefficient data of the correlation coefficient, and a correspondingcause of occurrence of the edge fluctuation in the line pattern for eachcandidate coefficient data.
 4. The system according to claim 1 wherein:the data processing system calculates a spatial frequency distributionof the edge fluctuation data.
 5. A system for measuring a pattern on asample, comprising: a data processing system that processes a set oftwo-dimensional distribution data of intensities of secondary electronsor reflected electrons from said sample, to calculate; a set of edgepoints indicative of positions of edges of said pattern in atwo-dimensional plane from said two-dimensional distribution data; anapproximation edge indicative of the edge of the pattern; an edgefluctuation data by calculating a difference between the set of edgepoints and said approximation edge; and a correlation between firstpotion of said edge fluctuation data and second portion of said edgefluctuation data; wherein the data processing system obtains the degreeof an edge fluctuation by calculating a standard deviation of the edgefluctuation data.
 6. The system according to claim 1, wherein: the dataprocessing system calculates a square root of an average ofroot-mean-square values of differences, each between a set of edgepoints derived with respect to a plurality of thresholds and theapproximation edge.
 7. A method for measuring a pattern on a sample,comprising: processing a set of two-dimensional distribution data ofintensities from the sample, to calculate: a set of edge pointsindicative of position of edges of said pattern in a two-dimensionalplane from said two-dimensional distribution data; an approximation edgeindicative of the edge of the pattern; an edge fluctuation data bycalculating a difference between the set of edge points and saidapproximation edge; and a correlation coefficient between a firstportion of the edge fluctuation data and a second portion of the edgefluctuation data.
 8. The method according to claim 7, wherein: saidpattern is a line pattern defined by a set of at least two edge points;and the processing includes calculating the correlation coefficientbetween the first portion of the edge fluctuation data for one side ofthe line pattern and the second portion of the edge fluctuation data foran opposite side of the line pattern.
 9. A method for measuring apattern on a sample, comprising: processing a set of two-dimensionaldistribution data of intensities from the sample, to calculate: a set ofedge points indicative of position of edges of said pattern in atwo-dimensional plane from said two-dimensional distribution data; an aapproximation edge indicative of the edge of the pattern; an edgefluctuation data by calculating a difference between the set of edgepoints and said approximation edge; and a correlation coefficientbetween a first portion of the edge fluctuation data and a secondportion of the edge fluctuation data storing, within a memory device, atable of candidate coefficient data of the correlation coefficient, anda corresponding cause of occurrence of the edge fluctuation in the linepattern for each candidate coefficient data.
 10. The method according toclaim 7, wherein: the processing calculates a spatial frequencydistribution of the edge fluctuation data.
 11. A method for measuring apattern on a sample, comprising; processing a set of two-dimensionaldistribution data of intensities from the sample, to calculate: a set ofedge points indicative of position of edges of said pattern in atwo-dimensional plane from said two-dimensional distribution data; anapproximation edge indicative of the edge of the pattern; an edgefluctuation data by calculating a difference between the set of edgepoints and said approximation edge; and a correlation between a firstportion of the edge fluctuation data and a second portion of the edgefluctuation data; wherein the processing obtains the degree of an edgefluctuation by calculating a standard deviation of the edge fluctuationdata.
 12. The method according to claim 7, wherein: the processingcalculates a square root of an average of root-mean-square values ofdifferences each between a set of edge points derived with respect to aplurality of thresholds and the approximation edge.
 13. Acomputer-readable medium having a sequence of computer implementableprogram code thereon, which when implemented, causes the computer toperform: processing a set of two-dimensional distribution data ofintensities from the sample, to calculate: a set of edge pointsindicative of position of edges of said pattern in a two-dimensionalplane from said two-dimensional distribution data; an approximation edgeindicative of the edge of the pattern; an edge fluctuation data bycalculating a difference between the set of edge points and saidapproximation edge; and a correlation coefficient between a firstportion of the edge fluctuation data and a second portion of the edgefluctuation data.
 14. The computer-readable medium according to claim13, wherein: said pattern is a line pattern defined by a set of at leasttwo edge points; and the processing includes calculating the correlationcoefficient between the first portion of the edge fluctuation data forone side of the line pattern and the second portion of the edgefluctuation data for an opposite side of the line pattern.
 15. Thecomputer-readable medium according to claim 14, wherein the sequence ofcomputer implementable program code, when implemented, causes thecomputer to: access a table having stored therein, candidate coefficientdata of the correlation coefficient, and a corresponding cause ofoccurrence of the edge fluctuation in the line, pattern for eachcandidate coefficient data.
 16. The computer-readable medium accordingto claim 13, wherein: the processing calculates a spatial frequencydistribution of the edge fluctuation data.
 17. The computer-readablemedium according to claim 13, wherein: the processing obtains the degreeof the edge fluctuation by calculating a standard deviation.
 18. Thecomputer-readable medium according to claim 13, wherein: the processingcalculates a square root of an average of root-mean-square values ofdifferences each between a set of edge points derived with respect to aplurality of thresholds and the approximation edge.
 19. A system formeasuring a pattern on a sample, according to claim 1, comprising: ascanning electron microscope for obtaining said set of two-dimensionaldistribution data of intensities.
 20. A system for measuring a patternon a sample, according to claim 5, comprising: a scanning electronmicroscope for obtaining said set of two-dimensional distribution dataof intensities.
 21. A system for measuring a pattern on a sample,according to claim 1, wherein the correlation coefficient is astatistically-calculated correlation coefficient.
 22. A system formeasuring a pattern on a sample, according to claim 5, wherein thecorrelation coefficient is a statistically-calculated correlationcoefficient.